I have done quite a bit of research online. I am now concluding that for me, I'm having two separate issues.
1. No audio sound - I had been talking to my sister earlier via speaker phone. Then when I tried to later call her normally, is when I couldn't hear her or a ring and the time counter was going. There seems to be a glitch with switching between headsets, speakers, siri and normal phone calls. I never use a headset, and didn't use Siri that day. It makes sense now....I couldn't hear anything when trying to call her, because she was the last person I called on speaker. Then when I called my niece (a new number) it worked fine. The next day I had the issue again when calling my husband, but I had been listening to music with my headphones on just prior to trying to call him. This must be a software issue that I hope Apple fixes ASAP.
2. Dropped calls / calls failed. I'm going to try what my friend (an Apple employee) suggested. He thinks because I restored my 4S from my old 3GS it's just exaggerating any issues I had on my old phone. He suggested I restore my phone, set it up as a new device, and then re-sync. Hopefully that will do the trick.